{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learning-lie-group-generators-from","title":"Learning Lie Group Generators from Trajectories","arxiv_id":"2504.03220","date":"2025-04-04","proceeding":null,"authors":["Lifan Hu"],"abstract":"This work investigates the inverse problem of generator recovery in matrix Lie groups from discretized trajectories. Let $G$ be a real matrix Lie group and $\\mathfrak{g} = \\text{Lie}(G)$ its corresponding Lie algebra. A smooth trajectory $\\gamma($t$)$ generated by a fixed Lie algebra element $\\xi \\in \\mathfrak{g}$ follows the exponential flow $\\gamma($t$) = g_0 \\cdot \\exp(t \\xi)$. The central task addressed in this work is the reconstruction of such a latent generator $\\xi$ from a discretized sequence of poses $ \\{g_0, g_1, \\dots, g_T\\} \\subset G$, sampled at uniform time intervals. This problem is formulated as a data-driven regression from normalized sequences of discrete Lie algebra increments $\\log\\left(g_{t}^{-1} g_{t+1}\\right)$ to the constant generator $\\xi \\in \\mathfrak{g}$. A feedforward neural network is trained to learn this mapping across several groups, including $\\text{SE(2)}, \\text{SE(3)}, \\text{SO(3)}, and \\text{SL(2,$\\mathbb{R})$}$. It demonstrates strong empirical accuracy under both clean and noisy conditions, which validates the viability of data-driven recovery of Lie group generators using shallow neural architectures. This is Lie-RL GitHub Repo https://github.com/Anormalm/LieRL-on-Trajectories. Feel free to make suggestions and collaborations!","url_abs":"https://arxiv.org/abs/2504.03220v1","url_pdf":"https://arxiv.org/pdf/2504.03220v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"learning-lie-group-generators-from","repo_url":"https://github.com/anormalm/lierl-on-trajectories","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}